MATEMATIČKI VESNIK
МАТЕМАТИЧКИ ВЕСНИК



MATEMATIČKI VESNIK
Existence of one weak solution for $p(x)$-biharmonic equations involving a concave-convex nonlinearity
R.A. Mashiyev, G. Alisoy, I. Ekincioglu

Abstract

In the present paper, using variational approach and the theory of the variable exponent Lebesgue spaces, the existence of nontrivial weak solutions to a fourth order elliptic equation involving a $p(x)$-biharmonic operator and a concave-convex nonlinearity the Navier boundary conditions is obtained.

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Keywords: Critical points; $p(x)$-biharmonic operator; Navier boundary conditions; concave-convex nonlinearities; Mountain Pass Theorem; Ekeland's variational principle.

MSC: 35J60, 35J48

Pages:  296--307     

Volume  69 ,  Issue  4 ,  2017